We present a new method for constructing simple ordinary abelian surfaces with a small embedding degree. To a quartic CM field K, we associate a quadric surface H ⊂ ℙ3(ℚ) and use its parametrization to determine Weil numbers in K corresponding in the sense of Honda-Tate theory to such surfaces. In general, the resulting surfaces have parameter ρ ≈ 8. However, if there exist rational lines on H, they can be used to achieve ρ ≈ 4. We give examples of non-primitive quartic CM fields such that H has rulings by rational lines. Furthermore, we show how our method can be used to construct parametric families of pairing-friendly surfaces. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Dryło, R. (2010). A new method for constructing pairing-friendly abelian surfaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6487 LNCS, pp. 298–311). https://doi.org/10.1007/978-3-642-17455-1_19
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